Structure Function Spectra and Acoustic Scattering Due to Homogeneous Isotropic Atmospheric Turbule Ensembles
Abstract
Expressions are derived for the spectral densities of the temperature and velocity structure functions of atmospheric turbulence, and for the corresponding Born approximation far field acoustic scattering cross sections, due to homogeneous isotropic stationary ensembles of self similar localized turbules having many different scale lengths. It is shown that for some range Kmin </= K </= Kmax' the inertial range, the spectral densities obey power laws with dependence K(-P)T, K(-P)v. The exponents (PT, Pv) depend only on choices of scaling relations and are independent of turbule morphology. Only Kmin', Kmax' and the values of the spectral densities outside the inertial range are morphology dependent. Expressions for Kmin and Kmax are derived in terms of inner and outer scale lengths in the turbule ensemble. If the turbule scale lengths a(alpha) are chosen to be in geometric sequence, and if the power law is given as PT=Pv=11/3, the Kolmogorov spectrum in the inertial range, then not only must the turbule velocity and temperature amplitudes scale as a (alpha, 1/3), the usual result, but also the turbule packing fractions must be independent of scale length. Expressions for the structure parameters (C2T,C2v) that occur in the usual Kolmogorov spectra are obtained in terms of the turbule model parameters. It is also shown that quasi Gaussian spectra result for the choice PT=Pv=0 and Gaussian turbule morphology.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1998
- Accession Number
- ADA351833
Entities
People
- George H. Goedecke
- Harry J. Auvermann
- Michael Deantonio
Organizations
- United States Army Research Laboratory